LMFDB - Embedded newform 6014.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.27880 q^{3} +1.00000 q^{4} +0.401675 q^{5} +3.27880 q^{6} -4.68111 q^{7} -1.00000 q^{8} +7.75051 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.27880 q^{3} +1.00000 q^{4} +0.401675 q^{5} +3.27880 q^{6} -4.68111 q^{7} -1.00000 q^{8} +7.75051 q^{9} -0.401675 q^{10} -1.05732 q^{11} -3.27880 q^{12} -6.56701 q^{13} +4.68111 q^{14} -1.31701 q^{15} +1.00000 q^{16} +5.05816 q^{17} -7.75051 q^{18} +4.70538 q^{19} +0.401675 q^{20} +15.3484 q^{21} +1.05732 q^{22} +5.86002 q^{23} +3.27880 q^{24} -4.83866 q^{25} +6.56701 q^{26} -15.5760 q^{27} -4.68111 q^{28} -2.64759 q^{29} +1.31701 q^{30} +1.00000 q^{31} -1.00000 q^{32} +3.46674 q^{33} -5.05816 q^{34} -1.88028 q^{35} +7.75051 q^{36} +2.11595 q^{37} -4.70538 q^{38} +21.5319 q^{39} -0.401675 q^{40} -4.13919 q^{41} -15.3484 q^{42} -11.0527 q^{43} -1.05732 q^{44} +3.11319 q^{45} -5.86002 q^{46} -6.65915 q^{47} -3.27880 q^{48} +14.9128 q^{49} +4.83866 q^{50} -16.5847 q^{51} -6.56701 q^{52} +13.5309 q^{53} +15.5760 q^{54} -0.424699 q^{55} +4.68111 q^{56} -15.4280 q^{57} +2.64759 q^{58} +5.66886 q^{59} -1.31701 q^{60} -10.5959 q^{61} -1.00000 q^{62} -36.2810 q^{63} +1.00000 q^{64} -2.63780 q^{65} -3.46674 q^{66} -13.1044 q^{67} +5.05816 q^{68} -19.2138 q^{69} +1.88028 q^{70} -12.2637 q^{71} -7.75051 q^{72} +1.67359 q^{73} -2.11595 q^{74} +15.8650 q^{75} +4.70538 q^{76} +4.94944 q^{77} -21.5319 q^{78} -12.1819 q^{79} +0.401675 q^{80} +27.8189 q^{81} +4.13919 q^{82} +0.247349 q^{83} +15.3484 q^{84} +2.03174 q^{85} +11.0527 q^{86} +8.68090 q^{87} +1.05732 q^{88} +17.0421 q^{89} -3.11319 q^{90} +30.7409 q^{91} +5.86002 q^{92} -3.27880 q^{93} +6.65915 q^{94} +1.89003 q^{95} +3.27880 q^{96} -1.00000 q^{97} -14.9128 q^{98} -8.19478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.27880	−1.89301	−0.946507	−	0.322683i	$-0.895415\pi$
$3$	−3.27880	−1.89301	−0.946507	+	0.322683i	$0.895415\pi$
$4$	1.00000	0.500000
$5$	0.401675	0.179634	0.0898172	−	0.995958i	$-0.471372\pi$
$5$	0.401675	0.179634	0.0898172	+	0.995958i	$0.471372\pi$
$6$	3.27880	1.33856
$7$	−4.68111	−1.76929	−0.884646	−	0.466263i	$-0.845600\pi$
$7$	−4.68111	−1.76929	−0.884646	+	0.466263i	$0.845600\pi$
$8$	−1.00000	−0.353553
$9$	7.75051	2.58350
$10$	−0.401675	−0.127021
$11$	−1.05732	−0.318794	−0.159397	−	0.987215i	$-0.550955\pi$
$11$	−1.05732	−0.318794	−0.159397	+	0.987215i	$0.550955\pi$
$12$	−3.27880	−0.946507
$13$	−6.56701	−1.82136	−0.910681	−	0.413110i	$-0.864442\pi$
$13$	−6.56701	−1.82136	−0.910681	+	0.413110i	$0.864442\pi$
$14$	4.68111	1.25108
$15$	−1.31701	−0.340051
$16$	1.00000	0.250000
$17$	5.05816	1.22678	0.613392	−	0.789779i	$-0.289805\pi$
$17$	5.05816	1.22678	0.613392	+	0.789779i	$0.289805\pi$
$18$	−7.75051	−1.82681
$19$	4.70538	1.07949	0.539744	−	0.841829i	$-0.318521\pi$
$19$	4.70538	1.07949	0.539744	+	0.841829i	$0.318521\pi$
$20$	0.401675	0.0898172
$21$	15.3484	3.34930
$22$	1.05732	0.225422
$23$	5.86002	1.22190	0.610950	−	0.791670i	$-0.290788\pi$
$23$	5.86002	1.22190	0.610950	+	0.791670i	$0.290788\pi$
$24$	3.27880	0.669282
$25$	−4.83866	−0.967731
$26$	6.56701	1.28790
$27$	−15.5760	−2.99759
$28$	−4.68111	−0.884646
$29$	−2.64759	−0.491644	−0.245822	−	0.969315i	$-0.579058\pi$
$29$	−2.64759	−0.491644	−0.245822	+	0.969315i	$0.579058\pi$
$30$	1.31701	0.240452
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	3.46674	0.603482
$34$	−5.05816	−0.867467
$35$	−1.88028	−0.317826
$36$	7.75051	1.29175
$37$	2.11595	0.347861	0.173930	−	0.984758i	$-0.444353\pi$
$37$	2.11595	0.347861	0.173930	+	0.984758i	$0.444353\pi$
$38$	−4.70538	−0.763314
$39$	21.5319	3.44786
$40$	−0.401675	−0.0635104
$41$	−4.13919	−0.646433	−0.323217	−	0.946325i	$-0.604764\pi$
$41$	−4.13919	−0.646433	−0.323217	+	0.946325i	$0.604764\pi$
$42$	−15.3484	−2.36831
$43$	−11.0527	−1.68552	−0.842759	−	0.538291i	$-0.819070\pi$
$43$	−11.0527	−1.68552	−0.842759	+	0.538291i	$0.819070\pi$
$44$	−1.05732	−0.159397
$45$	3.11319	0.464086
$46$	−5.86002	−0.864013
$47$	−6.65915	−0.971338	−0.485669	−	0.874143i	$-0.661424\pi$
$47$	−6.65915	−0.971338	−0.485669	+	0.874143i	$0.661424\pi$
$48$	−3.27880	−0.473254
$49$	14.9128	2.13040
$50$	4.83866	0.684289
$51$	−16.5847	−2.32232
$52$	−6.56701	−0.910681
$53$	13.5309	1.85862	0.929309	−	0.369303i	$-0.120403\pi$
$53$	13.5309	1.85862	0.929309	+	0.369303i	$0.120403\pi$
$54$	15.5760	2.11962
$55$	−0.424699	−0.0572665
$56$	4.68111	0.625539
$57$	−15.4280	−2.04349
$58$	2.64759	0.347645
$59$	5.66886	0.738023	0.369012	−	0.929425i	$-0.379696\pi$
$59$	5.66886	0.738023	0.369012	+	0.929425i	$0.379696\pi$
$60$	−1.31701	−0.170025
$61$	−10.5959	−1.35666	−0.678330	−	0.734757i	$-0.737296\pi$
$61$	−10.5959	−1.35666	−0.678330	+	0.734757i	$0.737296\pi$
$62$	−1.00000	−0.127000
$63$	−36.2810	−4.57097
$64$	1.00000	0.125000
$65$	−2.63780	−0.327179
$66$	−3.46674	−0.426727
$67$	−13.1044	−1.60095	−0.800476	−	0.599364i	$-0.795420\pi$
$67$	−13.1044	−1.60095	−0.800476	+	0.599364i	$0.795420\pi$
$68$	5.05816	0.613392
$69$	−19.2138	−2.31307
$70$	1.88028	0.224737
$71$	−12.2637	−1.45544	−0.727718	−	0.685877i	$-0.759419\pi$
$71$	−12.2637	−1.45544	−0.727718	+	0.685877i	$0.759419\pi$
$72$	−7.75051	−0.913406
$73$	1.67359	0.195879	0.0979394	−	0.995192i	$-0.468775\pi$
$73$	1.67359	0.195879	0.0979394	+	0.995192i	$0.468775\pi$
$74$	−2.11595	−0.245975
$75$	15.8650	1.83193
$76$	4.70538	0.539744
$77$	4.94944	0.564041
$78$	−21.5319	−2.43801
$79$	−12.1819	−1.37057	−0.685284	−	0.728276i	$-0.740322\pi$
$79$	−12.1819	−1.37057	−0.685284	+	0.728276i	$0.740322\pi$
$80$	0.401675	0.0449086
$81$	27.8189	3.09099
$82$	4.13919	0.457097
$83$	0.247349	0.0271501	0.0135750	−	0.999908i	$-0.495679\pi$
$83$	0.247349	0.0271501	0.0135750	+	0.999908i	$0.495679\pi$
$84$	15.3484	1.67465
$85$	2.03174	0.220373
$86$	11.0527	1.19184
$87$	8.68090	0.930690
$88$	1.05732	0.112711
$89$	17.0421	1.80645	0.903227	−	0.429162i	$-0.141191\pi$
$89$	17.0421	1.80645	0.903227	+	0.429162i	$0.141191\pi$
$90$	−3.11319	−0.328159
$91$	30.7409	3.22252
$92$	5.86002	0.610950
$93$	−3.27880	−0.339995
$94$	6.65915	0.686839
$95$	1.89003	0.193913
$96$	3.27880	0.334641
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−14.9128	−1.50642
$99$	−8.19478	−0.823606
$100$	−4.83866	−0.483866
$101$	4.14442	0.412385	0.206192	−	0.978511i	$-0.433893\pi$
$101$	4.14442	0.412385	0.206192	+	0.978511i	$0.433893\pi$
$102$	16.5847	1.64213
$103$	−13.2527	−1.30582	−0.652912	−	0.757434i	$-0.726453\pi$
$103$	−13.2527	−1.30582	−0.652912	+	0.757434i	$0.726453\pi$
$104$	6.56701	0.643949
$105$	6.16507	0.601649
$106$	−13.5309	−1.31424
$107$	3.99724	0.386428	0.193214	−	0.981157i	$-0.438109\pi$
$107$	3.99724	0.386428	0.193214	+	0.981157i	$0.438109\pi$
$108$	−15.5760	−1.49880
$109$	−2.03855	−0.195258	−0.0976291	−	0.995223i	$-0.531126\pi$
$109$	−2.03855	−0.195258	−0.0976291	+	0.995223i	$0.531126\pi$
$110$	0.424699	0.0404935
$111$	−6.93778	−0.658505
$112$	−4.68111	−0.442323
$113$	−10.5049	−0.988220	−0.494110	−	0.869399i	$-0.664506\pi$
$113$	−10.5049	−0.988220	−0.494110	+	0.869399i	$0.664506\pi$
$114$	15.4280	1.44496
$115$	2.35382	0.219495
$116$	−2.64759	−0.245822
$117$	−50.8977	−4.70549
$118$	−5.66886	−0.521861
$119$	−23.6778	−2.17054
$120$	1.31701	0.120226
$121$	−9.88207	−0.898370
$122$	10.5959	0.959304
$123$	13.5716	1.22371
$124$	1.00000	0.0898027
$125$	−3.95194	−0.353472
$126$	36.2810	3.23217
$127$	1.78089	0.158028	0.0790141	−	0.996874i	$-0.474823\pi$
$127$	1.78089	0.158028	0.0790141	+	0.996874i	$0.474823\pi$
$128$	−1.00000	−0.0883883
$129$	36.2395	3.19071
$130$	2.63780	0.231351
$131$	2.70870	0.236660	0.118330	−	0.992974i	$-0.462246\pi$
$131$	2.70870	0.236660	0.118330	+	0.992974i	$0.462246\pi$
$132$	3.46674	0.301741
$133$	−22.0264	−1.90993
$134$	13.1044	1.13204
$135$	−6.25647	−0.538471
$136$	−5.05816	−0.433734
$137$	7.56941	0.646698	0.323349	−	0.946280i	$-0.395191\pi$
$137$	7.56941	0.646698	0.323349	+	0.946280i	$0.395191\pi$
$138$	19.2138	1.63559
$139$	−14.9491	−1.26796	−0.633981	−	0.773349i	$-0.718580\pi$
$139$	−14.9491	−1.26796	−0.633981	+	0.773349i	$0.718580\pi$
$140$	−1.88028	−0.158913
$141$	21.8340	1.83876
$142$	12.2637	1.02915
$143$	6.94345	0.580640
$144$	7.75051	0.645876
$145$	−1.06347	−0.0883163
$146$	−1.67359	−0.138507
$147$	−48.8960	−4.03287
$148$	2.11595	0.173930
$149$	−4.68878	−0.384120	−0.192060	−	0.981383i	$-0.561517\pi$
$149$	−4.68878	−0.384120	−0.192060	+	0.981383i	$0.561517\pi$
$150$	−15.8650	−1.29537
$151$	−4.61548	−0.375602	−0.187801	−	0.982207i	$-0.560136\pi$
$151$	−4.61548	−0.375602	−0.187801	+	0.982207i	$0.560136\pi$
$152$	−4.70538	−0.381657
$153$	39.2033	3.16940
$154$	−4.94944	−0.398837
$155$	0.401675	0.0322633
$156$	21.5319	1.72393
$157$	−2.71143	−0.216396	−0.108198	−	0.994129i	$-0.534508\pi$
$157$	−2.71143	−0.216396	−0.108198	+	0.994129i	$0.534508\pi$
$158$	12.1819	0.969137
$159$	−44.3652	−3.51839
$160$	−0.401675	−0.0317552
$161$	−27.4314	−2.16190
$162$	−27.8189	−2.18566
$163$	−12.0106	−0.940743	−0.470372	−	0.882468i	$-0.655880\pi$
$163$	−12.0106	−0.940743	−0.470372	+	0.882468i	$0.655880\pi$
$164$	−4.13919	−0.323217
$165$	1.39250	0.108406
$166$	−0.247349	−0.0191980
$167$	−11.9633	−0.925752	−0.462876	−	0.886423i	$-0.653182\pi$
$167$	−11.9633	−0.925752	−0.462876	+	0.886423i	$0.653182\pi$
$168$	−15.3484	−1.18416
$169$	30.1257	2.31736
$170$	−2.03174	−0.155827
$171$	36.4691	2.78886
$172$	−11.0527	−0.842759
$173$	9.13150	0.694255	0.347127	−	0.937818i	$-0.387157\pi$
$173$	9.13150	0.694255	0.347127	+	0.937818i	$0.387157\pi$
$174$	−8.68090	−0.658097
$175$	22.6503	1.71220
$176$	−1.05732	−0.0796986
$177$	−18.5870	−1.39709
$178$	−17.0421	−1.27736
$179$	−8.70893	−0.650936	−0.325468	−	0.945553i	$-0.605522\pi$
$179$	−8.70893	−0.650936	−0.325468	+	0.945553i	$0.605522\pi$
$180$	3.11319	0.232043
$181$	−18.4507	−1.37143	−0.685716	−	0.727870i	$-0.740511\pi$
$181$	−18.4507	−1.37143	−0.685716	+	0.727870i	$0.740511\pi$
$182$	−30.7409	−2.27867
$183$	34.7417	2.56818
$184$	−5.86002	−0.432007
$185$	0.849926	0.0624878
$186$	3.27880	0.240413
$187$	−5.34810	−0.391092
$188$	−6.65915	−0.485669
$189$	72.9127	5.30362
$190$	−1.89003	−0.137117
$191$	4.47412	0.323736	0.161868	−	0.986812i	$-0.448248\pi$
$191$	4.47412	0.323736	0.161868	+	0.986812i	$0.448248\pi$
$192$	−3.27880	−0.236627
$193$	2.94492	0.211980	0.105990	−	0.994367i	$-0.466199\pi$
$193$	2.94492	0.211980	0.105990	+	0.994367i	$0.466199\pi$
$194$	1.00000	0.0717958
$195$	8.64883	0.619355
$196$	14.9128	1.06520
$197$	−26.3151	−1.87488	−0.937438	−	0.348153i	$-0.886809\pi$
$197$	−26.3151	−1.87488	−0.937438	+	0.348153i	$0.886809\pi$
$198$	8.19478	0.582378
$199$	23.3659	1.65636	0.828182	−	0.560459i	$-0.189375\pi$
$199$	23.3659	1.65636	0.828182	+	0.560459i	$0.189375\pi$
$200$	4.83866	0.342145
$201$	42.9665	3.03063
$202$	−4.14442	−0.291600
$203$	12.3936	0.869863
$204$	−16.5847	−1.16116
$205$	−1.66261	−0.116122
$206$	13.2527	0.923357
$207$	45.4182	3.15678
$208$	−6.56701	−0.455340
$209$	−4.97510	−0.344135
$210$	−6.16507	−0.425430
$211$	11.4085	0.785391	0.392696	−	0.919668i	$-0.371543\pi$
$211$	11.4085	0.785391	0.392696	+	0.919668i	$0.371543\pi$
$212$	13.5309	0.929309
$213$	40.2102	2.75516
$214$	−3.99724	−0.273246
$215$	−4.43959	−0.302777
$216$	15.5760	1.05981
$217$	−4.68111	−0.317774
$218$	2.03855	0.138068
$219$	−5.48736	−0.370801
$220$	−0.424699	−0.0286332
$221$	−33.2170	−2.23442
$222$	6.93778	0.465634
$223$	−23.4364	−1.56942	−0.784710	−	0.619864i	$-0.787188\pi$
$223$	−23.4364	−1.56942	−0.784710	+	0.619864i	$0.787188\pi$
$224$	4.68111	0.312770
$225$	−37.5021	−2.50014
$226$	10.5049	0.698777
$227$	−1.44043	−0.0956049	−0.0478025	−	0.998857i	$-0.515222\pi$
$227$	−1.44043	−0.0956049	−0.0478025	+	0.998857i	$0.515222\pi$
$228$	−15.4280	−1.02174
$229$	−2.97428	−0.196546	−0.0982729	−	0.995160i	$-0.531332\pi$
$229$	−2.97428	−0.196546	−0.0982729	+	0.995160i	$0.531332\pi$
$230$	−2.35382	−0.155207
$231$	−16.2282	−1.06774
$232$	2.64759	0.173822
$233$	9.96797	0.653024	0.326512	−	0.945193i	$-0.394127\pi$
$233$	9.96797	0.653024	0.326512	+	0.945193i	$0.394127\pi$
$234$	50.8977	3.32729
$235$	−2.67482	−0.174486
$236$	5.66886	0.369012
$237$	39.9419	2.59450
$238$	23.6778	1.53480
$239$	6.50679	0.420889	0.210445	−	0.977606i	$-0.432509\pi$
$239$	6.50679	0.420889	0.210445	+	0.977606i	$0.432509\pi$
$240$	−1.31701	−0.0850127
$241$	−5.39219	−0.347342	−0.173671	−	0.984804i	$-0.555563\pi$
$241$	−5.39219	−0.347342	−0.173671	+	0.984804i	$0.555563\pi$
$242$	9.88207	0.635244
$243$	−44.4846	−2.85369
$244$	−10.5959	−0.678330
$245$	5.99009	0.382693
$246$	−13.5716	−0.865292
$247$	−30.9003	−1.96614
$248$	−1.00000	−0.0635001
$249$	−0.811007	−0.0513955
$250$	3.95194	0.249943
$251$	−17.7199	−1.11847	−0.559236	−	0.829009i	$-0.688905\pi$
$251$	−17.7199	−1.11847	−0.559236	+	0.829009i	$0.688905\pi$
$252$	−36.2810	−2.28549
$253$	−6.19593	−0.389535
$254$	−1.78089	−0.111743
$255$	−6.66165	−0.417169
$256$	1.00000	0.0625000
$257$	−7.49589	−0.467581	−0.233790	−	0.972287i	$-0.575113\pi$
$257$	−7.49589	−0.467581	−0.233790	+	0.972287i	$0.575113\pi$
$258$	−36.2395	−2.25617
$259$	−9.90501	−0.615467
$260$	−2.63780	−0.163590
$261$	−20.5201	−1.27016
$262$	−2.70870	−0.167344
$263$	10.8783	0.670784	0.335392	−	0.942079i	$-0.391131\pi$
$263$	10.8783	0.670784	0.335392	+	0.942079i	$0.391131\pi$
$264$	−3.46674	−0.213363
$265$	5.43504	0.333872
$266$	22.0264	1.35053
$267$	−55.8775	−3.41964
$268$	−13.1044	−0.800476
$269$	−17.6754	−1.07769	−0.538843	−	0.842406i	$-0.681138\pi$
$269$	−17.6754	−1.07769	−0.538843	+	0.842406i	$0.681138\pi$
$270$	6.25647	0.380757
$271$	0.0598523	0.00363577	0.00181788	−	0.999998i	$-0.499421\pi$
$271$	0.0598523	0.00363577	0.00181788	+	0.999998i	$0.499421\pi$
$272$	5.05816	0.306696
$273$	−100.793	−6.10028
$274$	−7.56941	−0.457285
$275$	5.11602	0.308507
$276$	−19.2138	−1.15654
$277$	−25.6803	−1.54298	−0.771490	−	0.636241i	$-0.780488\pi$
$277$	−25.6803	−1.54298	−0.771490	+	0.636241i	$0.780488\pi$
$278$	14.9491	0.896584
$279$	7.75051	0.464011
$280$	1.88028	0.112368
$281$	23.6350	1.40995	0.704973	−	0.709234i	$-0.250959\pi$
$281$	23.6350	1.40995	0.704973	+	0.709234i	$0.250959\pi$
$282$	−21.8340	−1.30020
$283$	−3.76699	−0.223924	−0.111962	−	0.993712i	$-0.535714\pi$
$283$	−3.76699	−0.223924	−0.111962	+	0.993712i	$0.535714\pi$
$284$	−12.2637	−0.727718
$285$	−6.19704	−0.367081
$286$	−6.94345	−0.410575
$287$	19.3760	1.14373
$288$	−7.75051	−0.456703
$289$	8.58499	0.505000
$290$	1.06347	0.0624490
$291$	3.27880	0.192206
$292$	1.67359	0.0979394
$293$	29.4029	1.71774	0.858868	−	0.512198i	$-0.171168\pi$
$293$	29.4029	1.71774	0.858868	+	0.512198i	$0.171168\pi$
$294$	48.8960	2.85167
$295$	2.27704	0.132574
$296$	−2.11595	−0.122987
$297$	16.4688	0.955616
$298$	4.68878	0.271614
$299$	−38.4828	−2.22552
$300$	15.8650	0.915965
$301$	51.7388	2.98218
$302$	4.61548	0.265591
$303$	−13.5887	−0.780650
$304$	4.70538	0.269872
$305$	−4.25609	−0.243703
$306$	−39.2033	−2.24111
$307$	−27.3504	−1.56097	−0.780484	−	0.625175i	$-0.785027\pi$
$307$	−27.3504	−1.56097	−0.780484	+	0.625175i	$0.785027\pi$
$308$	4.94944	0.282020
$309$	43.4528	2.47194
$310$	−0.401675	−0.0228136
$311$	31.1663	1.76728	0.883641	−	0.468166i	$-0.155085\pi$
$311$	31.1663	1.76728	0.883641	+	0.468166i	$0.155085\pi$
$312$	−21.5319	−1.21900
$313$	4.98021	0.281498	0.140749	−	0.990045i	$-0.455049\pi$
$313$	4.98021	0.281498	0.140749	+	0.990045i	$0.455049\pi$
$314$	2.71143	0.153015
$315$	−14.5732	−0.821104
$316$	−12.1819	−0.685284
$317$	−28.6217	−1.60755	−0.803776	−	0.594932i	$-0.797179\pi$
$317$	−28.6217	−1.60755	−0.803776	+	0.594932i	$0.797179\pi$
$318$	44.3652	2.48788
$319$	2.79935	0.156733
$320$	0.401675	0.0224543
$321$	−13.1062	−0.731514
$322$	27.4314	1.52869
$323$	23.8006	1.32430
$324$	27.8189	1.54549
$325$	31.7755	1.76259
$326$	12.0106	0.665206
$327$	6.68401	0.369626
$328$	4.13919	0.228549
$329$	31.1722	1.71858
$330$	−1.39250	−0.0766548
$331$	−16.3254	−0.897327	−0.448663	−	0.893701i	$-0.648100\pi$
$331$	−16.3254	−0.897327	−0.448663	+	0.893701i	$0.648100\pi$
$332$	0.247349	0.0135750
$333$	16.3997	0.898699
$334$	11.9633	0.654605
$335$	−5.26369	−0.287586
$336$	15.3484	0.837324
$337$	9.42295	0.513301	0.256651	−	0.966504i	$-0.417381\pi$
$337$	9.42295	0.513301	0.256651	+	0.966504i	$0.417381\pi$
$338$	−30.1257	−1.63862
$339$	34.4435	1.87072
$340$	2.03174	0.110186
$341$	−1.05732	−0.0572572
$342$	−36.4691	−1.97202
$343$	−37.0406	−2.00000
$344$	11.0527	0.595921
$345$	−7.71771	−0.415508
$346$	−9.13150	−0.490912
$347$	19.2622	1.03405	0.517025	−	0.855970i	$-0.327039\pi$
$347$	19.2622	1.03405	0.517025	+	0.855970i	$0.327039\pi$
$348$	8.68090	0.465345
$349$	23.1715	1.24034	0.620171	−	0.784467i	$-0.287063\pi$
$349$	23.1715	1.24034	0.620171	+	0.784467i	$0.287063\pi$
$350$	−22.6503	−1.21071
$351$	102.288	5.45970
$352$	1.05732	0.0563554
$353$	16.8980	0.899387	0.449694	−	0.893183i	$-0.351533\pi$
$353$	16.8980	0.899387	0.449694	+	0.893183i	$0.351533\pi$
$354$	18.5870	0.987890
$355$	−4.92603	−0.261446
$356$	17.0421	0.903227
$357$	77.6347	4.10886
$358$	8.70893	0.460281
$359$	8.77235	0.462987	0.231493	−	0.972836i	$-0.425639\pi$
$359$	8.77235	0.462987	0.231493	+	0.972836i	$0.425639\pi$
$360$	−3.11319	−0.164079
$361$	3.14061	0.165295
$362$	18.4507	0.969748
$363$	32.4013	1.70063
$364$	30.7409	1.61126
$365$	0.672239	0.0351866
$366$	−34.7417	−1.81598
$367$	−6.53698	−0.341228	−0.170614	−	0.985338i	$-0.554575\pi$
$367$	−6.53698	−0.341228	−0.170614	+	0.985338i	$0.554575\pi$
$368$	5.86002	0.305475
$369$	−32.0808	−1.67006
$370$	−0.849926	−0.0441855
$371$	−63.3398	−3.28844
$372$	−3.27880	−0.169998
$373$	13.6132	0.704865	0.352433	−	0.935837i	$-0.385355\pi$
$373$	13.6132	0.704865	0.352433	+	0.935837i	$0.385355\pi$
$374$	5.34810	0.276544
$375$	12.9576	0.669128
$376$	6.65915	0.343420
$377$	17.3867	0.895462
$378$	−72.9127	−3.75023
$379$	20.7333	1.06500	0.532500	−	0.846430i	$-0.321253\pi$
$379$	20.7333	1.06500	0.532500	+	0.846430i	$0.321253\pi$
$380$	1.89003	0.0969567
$381$	−5.83916	−0.299149
$382$	−4.47412	−0.228916
$383$	32.9367	1.68299	0.841494	−	0.540266i	$-0.181676\pi$
$383$	32.9367	1.68299	0.841494	+	0.540266i	$0.181676\pi$
$384$	3.27880	0.167320
$385$	1.98806	0.101321
$386$	−2.94492	−0.149892
$387$	−85.6639	−4.35454
$388$	−1.00000	−0.0507673
$389$	−25.1038	−1.27282	−0.636408	−	0.771353i	$-0.719580\pi$
$389$	−25.1038	−1.27282	−0.636408	+	0.771353i	$0.719580\pi$
$390$	−8.64883	−0.437950
$391$	29.6409	1.49901
$392$	−14.9128	−0.753209
$393$	−8.88128	−0.448001
$394$	26.3151	1.32574
$395$	−4.89315	−0.246201
$396$	−8.19478	−0.411803
$397$	30.2272	1.51706	0.758530	−	0.651638i	$-0.225918\pi$
$397$	30.2272	1.51706	0.758530	+	0.651638i	$0.225918\pi$
$398$	−23.3659	−1.17123
$399$	72.2201	3.61553
$400$	−4.83866	−0.241933
$401$	8.93328	0.446107	0.223053	−	0.974806i	$-0.428398\pi$
$401$	8.93328	0.446107	0.223053	+	0.974806i	$0.428398\pi$
$402$	−42.9665	−2.14298
$403$	−6.56701	−0.327126
$404$	4.14442	0.206192
$405$	11.1741	0.555248
$406$	−12.3936	−0.615086
$407$	−2.23724	−0.110896
$408$	16.5847	0.821064
$409$	3.18372	0.157425	0.0787125	−	0.996897i	$-0.474919\pi$
$409$	3.18372	0.157425	0.0787125	+	0.996897i	$0.474919\pi$
$410$	1.66261	0.0821104
$411$	−24.8185	−1.22421
$412$	−13.2527	−0.652912
$413$	−26.5366	−1.30578
$414$	−45.4182	−2.23218
$415$	0.0993538	0.00487709
$416$	6.56701	0.321974
$417$	49.0149	2.40027
$418$	4.97510	0.243340
$419$	29.5038	1.44135	0.720677	−	0.693271i	$-0.243831\pi$
$419$	29.5038	1.44135	0.720677	+	0.693271i	$0.243831\pi$
$420$	6.16507	0.300825
$421$	20.6485	1.00635	0.503174	−	0.864185i	$-0.332166\pi$
$421$	20.6485	1.00635	0.503174	+	0.864185i	$0.332166\pi$
$422$	−11.4085	−0.555356
$423$	−51.6118	−2.50945
$424$	−13.5309	−0.657121
$425$	−24.4747	−1.18720
$426$	−40.2102	−1.94819
$427$	49.6004	2.40033
$428$	3.99724	0.193214
$429$	−22.7661	−1.09916
$430$	4.43959	0.214096
$431$	−15.4316	−0.743315	−0.371658	−	0.928370i	$-0.621210\pi$
$431$	−15.4316	−0.743315	−0.371658	+	0.928370i	$0.621210\pi$
$432$	−15.5760	−0.749399
$433$	−9.70789	−0.466531	−0.233266	−	0.972413i	$-0.574941\pi$
$433$	−9.70789	−0.466531	−0.233266	+	0.972413i	$0.574941\pi$
$434$	4.68111	0.224700
$435$	3.48690	0.167184
$436$	−2.03855	−0.0976291
$437$	27.5736	1.31903
$438$	5.48736	0.262196
$439$	25.7483	1.22890	0.614450	−	0.788956i	$-0.289378\pi$
$439$	25.7483	1.22890	0.614450	+	0.788956i	$0.289378\pi$
$440$	0.424699	0.0202468
$441$	115.582	5.50389
$442$	33.2170	1.57997
$443$	−6.05812	−0.287830	−0.143915	−	0.989590i	$-0.545969\pi$
$443$	−6.05812	−0.287830	−0.143915	+	0.989590i	$0.545969\pi$
$444$	−6.93778	−0.329253
$445$	6.84537	0.324502
$446$	23.4364	1.10975
$447$	15.3736	0.727144
$448$	−4.68111	−0.221162
$449$	−8.55022	−0.403510	−0.201755	−	0.979436i	$-0.564664\pi$
$449$	−8.55022	−0.403510	−0.201755	+	0.979436i	$0.564664\pi$
$450$	37.5021	1.76786
$451$	4.37646	0.206079
$452$	−10.5049	−0.494110
$453$	15.1332	0.711020
$454$	1.44043	0.0676029
$455$	12.3478	0.578876
$456$	15.4280	0.722482
$457$	32.4658	1.51868	0.759342	−	0.650691i	$-0.225521\pi$
$457$	32.4658	1.51868	0.759342	+	0.650691i	$0.225521\pi$
$458$	2.97428	0.138979
$459$	−78.7857	−3.67740
$460$	2.35382	0.109748
$461$	19.7026	0.917640	0.458820	−	0.888529i	$-0.348272\pi$
$461$	19.7026	0.917640	0.458820	+	0.888529i	$0.348272\pi$
$462$	16.2282	0.755004
$463$	−13.8858	−0.645328	−0.322664	−	0.946514i	$-0.604578\pi$
$463$	−13.8858	−0.645328	−0.322664	+	0.946514i	$0.604578\pi$
$464$	−2.64759	−0.122911
$465$	−1.31701	−0.0610749
$466$	−9.96797	−0.461757
$467$	24.8547	1.15014	0.575069	−	0.818105i	$-0.304975\pi$
$467$	24.8547	1.15014	0.575069	+	0.818105i	$0.304975\pi$
$468$	−50.8977	−2.35275
$469$	61.3429	2.83255
$470$	2.67482	0.123380
$471$	8.89024	0.409641
$472$	−5.66886	−0.260931
$473$	11.6862	0.537334
$474$	−39.9419	−1.83459
$475$	−22.7677	−1.04465
$476$	−23.6778	−1.08527
$477$	104.872	4.80175
$478$	−6.50679	−0.297614
$479$	−25.2636	−1.15432	−0.577162	−	0.816630i	$-0.695840\pi$
$479$	−25.2636	−1.15432	−0.577162	+	0.816630i	$0.695840\pi$
$480$	1.31701	0.0601130
$481$	−13.8955	−0.633580
$482$	5.39219	0.245608
$483$	89.9420	4.09250
$484$	−9.88207	−0.449185
$485$	−0.401675	−0.0182391
$486$	44.4846	2.01786
$487$	11.7642	0.533088	0.266544	−	0.963823i	$-0.414118\pi$
$487$	11.7642	0.533088	0.266544	+	0.963823i	$0.414118\pi$
$488$	10.5959	0.479652
$489$	39.3803	1.78084
$490$	−5.99009	−0.270605
$491$	−22.4750	−1.01428	−0.507141	−	0.861863i	$-0.669298\pi$
$491$	−22.4750	−1.01428	−0.507141	+	0.861863i	$0.669298\pi$
$492$	13.5716	0.611854
$493$	−13.3919	−0.603141
$494$	30.9003	1.39027
$495$	−3.29164	−0.147948
$496$	1.00000	0.0449013
$497$	57.4078	2.57509
$498$	0.811007	0.0363421
$499$	13.1115	0.586949	0.293475	−	0.955967i	$-0.405188\pi$
$499$	13.1115	0.586949	0.293475	+	0.955967i	$0.405188\pi$
$500$	−3.95194	−0.176736
$501$	39.2254	1.75246
$502$	17.7199	0.790879
$503$	−34.5711	−1.54145	−0.770725	−	0.637168i	$-0.780106\pi$
$503$	−34.5711	−1.54145	−0.770725	+	0.637168i	$0.780106\pi$
$504$	36.2810	1.61608
$505$	1.66471	0.0740785
$506$	6.19593	0.275443
$507$	−98.7760	−4.38679
$508$	1.78089	0.0790141
$509$	−15.3095	−0.678583	−0.339292	−	0.940681i	$-0.610187\pi$
$509$	−15.3095	−0.678583	−0.339292	+	0.940681i	$0.610187\pi$
$510$	6.66165	0.294983
$511$	−7.83425	−0.346567
$512$	−1.00000	−0.0441942
$513$	−73.2908	−3.23587
$514$	7.49589	0.330630
$515$	−5.32326	−0.234571
$516$	36.2395	1.59536
$517$	7.04087	0.309657
$518$	9.90501	0.435201
$519$	−29.9403	−1.31423
$520$	2.63780	0.115675
$521$	−14.3812	−0.630050	−0.315025	−	0.949083i	$-0.602013\pi$
$521$	−14.3812	−0.630050	−0.315025	+	0.949083i	$0.602013\pi$
$522$	20.5201	0.898142
$523$	10.9928	0.480682	0.240341	−	0.970688i	$-0.422741\pi$
$523$	10.9928	0.480682	0.240341	+	0.970688i	$0.422741\pi$
$524$	2.70870	0.118330
$525$	−74.2657	−3.24122
$526$	−10.8783	−0.474316
$527$	5.05816	0.220337
$528$	3.46674	0.150871
$529$	11.3399	0.493037
$530$	−5.43504	−0.236083
$531$	43.9366	1.90668
$532$	−22.0264	−0.954965
$533$	27.1821	1.17739
$534$	55.8775	2.41805
$535$	1.60559	0.0694158
$536$	13.1044	0.566022
$537$	28.5548	1.23223
$538$	17.6754	0.762039
$539$	−15.7676	−0.679159
$540$	−6.25647	−0.269236
$541$	17.5395	0.754081	0.377040	−	0.926197i	$-0.376942\pi$
$541$	17.5395	0.754081	0.377040	+	0.926197i	$0.376942\pi$
$542$	−0.0598523	−0.00257087
$543$	60.4962	2.59614
$544$	−5.05816	−0.216867
$545$	−0.818836	−0.0350751
$546$	100.793	4.31355
$547$	−9.77269	−0.417850	−0.208925	−	0.977932i	$-0.566996\pi$
$547$	−9.77269	−0.417850	−0.208925	+	0.977932i	$0.566996\pi$
$548$	7.56941	0.323349
$549$	−82.1233	−3.50494
$550$	−5.11602	−0.218148
$551$	−12.4579	−0.530724
$552$	19.2138	0.817795
$553$	57.0246	2.42493
$554$	25.6803	1.09105
$555$	−2.78673	−0.118290
$556$	−14.9491	−0.633981
$557$	5.84953	0.247853	0.123926	−	0.992291i	$-0.460451\pi$
$557$	5.84953	0.247853	0.123926	+	0.992291i	$0.460451\pi$
$558$	−7.75051	−0.328105
$559$	72.5831	3.06994
$560$	−1.88028	−0.0794565
$561$	17.5353	0.740343
$562$	−23.6350	−0.996983
$563$	3.76729	0.158772	0.0793862	−	0.996844i	$-0.474704\pi$
$563$	3.76729	0.158772	0.0793862	+	0.996844i	$0.474704\pi$
$564$	21.8340	0.919378
$565$	−4.21957	−0.177518
$566$	3.76699	0.158338
$567$	−130.223	−5.46886
$568$	12.2637	0.514574
$569$	−5.88634	−0.246768	−0.123384	−	0.992359i	$-0.539375\pi$
$569$	−5.88634	−0.246768	−0.123384	+	0.992359i	$0.539375\pi$
$570$	6.19704	0.259565
$571$	−30.5778	−1.27964	−0.639821	−	0.768524i	$-0.720991\pi$
$571$	−30.5778	−1.27964	−0.639821	+	0.768524i	$0.720991\pi$
$572$	6.94345	0.290320
$573$	−14.6697	−0.612836
$574$	−19.3760	−0.808739
$575$	−28.3546	−1.18247
$576$	7.75051	0.322938
$577$	23.7860	0.990225	0.495113	−	0.868829i	$-0.335127\pi$
$577$	23.7860	0.990225	0.495113	+	0.868829i	$0.335127\pi$
$578$	−8.58499	−0.357089
$579$	−9.65578	−0.401281
$580$	−1.06347	−0.0441581
$581$	−1.15787	−0.0480364
$582$	−3.27880	−0.135911
$583$	−14.3066	−0.592517
$584$	−1.67359	−0.0692536
$585$	−20.4443	−0.845269
$586$	−29.4029	−1.21462
$587$	0.822667	0.0339551	0.0169776	−	0.999856i	$-0.494596\pi$
$587$	0.822667	0.0339551	0.0169776	+	0.999856i	$0.494596\pi$
$588$	−48.8960	−2.01644
$589$	4.70538	0.193882
$590$	−2.27704	−0.0937442
$591$	86.2820	3.54917
$592$	2.11595	0.0869652
$593$	35.3169	1.45029	0.725146	−	0.688595i	$-0.241772\pi$
$593$	35.3169	1.45029	0.725146	+	0.688595i	$0.241772\pi$
$594$	−16.4688	−0.675723
$595$	−9.51078	−0.389904
$596$	−4.68878	−0.192060
$597$	−76.6120	−3.13552
$598$	38.4828	1.57368
$599$	39.9627	1.63283	0.816415	−	0.577465i	$-0.195958\pi$
$599$	39.9627	1.63283	0.816415	+	0.577465i	$0.195958\pi$
$600$	−15.8650	−0.647685
$601$	−34.4612	−1.40570	−0.702850	−	0.711338i	$-0.748090\pi$
$601$	−34.4612	−1.40570	−0.702850	+	0.711338i	$0.748090\pi$
$602$	−51.7388	−2.10872
$603$	−101.565	−4.13607
$604$	−4.61548	−0.187801
$605$	−3.96938	−0.161378
$606$	13.5887	0.552003
$607$	38.5846	1.56610	0.783051	−	0.621958i	$-0.213662\pi$
$607$	38.5846	1.56610	0.783051	+	0.621958i	$0.213662\pi$
$608$	−4.70538	−0.190828
$609$	−40.6362	−1.64666
$610$	4.25609	0.172324
$611$	43.7308	1.76916
$612$	39.2033	1.58470
$613$	5.40571	0.218335	0.109167	−	0.994023i	$-0.465182\pi$
$613$	5.40571	0.218335	0.109167	+	0.994023i	$0.465182\pi$
$614$	27.3504	1.10377
$615$	5.45136	0.219820
$616$	−4.94944	−0.199418
$617$	17.4467	0.702376	0.351188	−	0.936305i	$-0.385778\pi$
$617$	17.4467	0.702376	0.351188	+	0.936305i	$0.385778\pi$
$618$	−43.4528	−1.74793
$619$	35.5308	1.42810	0.714051	−	0.700093i	$-0.246858\pi$
$619$	35.5308	1.42810	0.714051	+	0.700093i	$0.246858\pi$
$620$	0.401675	0.0161317
$621$	−91.2755	−3.66276
$622$	−31.1663	−1.24966
$623$	−79.7757	−3.19615
$624$	21.5319	0.861966
$625$	22.6059	0.904236
$626$	−4.98021	−0.199049
$627$	16.3123	0.651452
$628$	−2.71143	−0.108198
$629$	10.7028	0.426750
$630$	14.5732	0.580608
$631$	−28.4881	−1.13409	−0.567046	−	0.823686i	$-0.691914\pi$
$631$	−28.4881	−1.13409	−0.567046	+	0.823686i	$0.691914\pi$
$632$	12.1819	0.484569
$633$	−37.4061	−1.48676
$634$	28.6217	1.13671
$635$	0.715337	0.0283873
$636$	−44.3652	−1.75920
$637$	−97.9324	−3.88022
$638$	−2.79935	−0.110827
$639$	−95.0501	−3.76012
$640$	−0.401675	−0.0158776
$641$	37.7633	1.49156	0.745780	−	0.666192i	$-0.232077\pi$
$641$	37.7633	1.49156	0.745780	+	0.666192i	$0.232077\pi$
$642$	13.1062	0.517259
$643$	46.1701	1.82077	0.910385	−	0.413762i	$-0.135786\pi$
$643$	46.1701	1.82077	0.910385	+	0.413762i	$0.135786\pi$
$644$	−27.4314	−1.08095
$645$	14.5565	0.573162
$646$	−23.8006	−0.936421
$647$	−3.03322	−0.119248	−0.0596242	−	0.998221i	$-0.518990\pi$
$647$	−3.03322	−0.119248	−0.0596242	+	0.998221i	$0.518990\pi$
$648$	−27.8189	−1.09283
$649$	−5.99381	−0.235278
$650$	−31.7755	−1.24634
$651$	15.3484	0.601551
$652$	−12.0106	−0.470372
$653$	−19.1522	−0.749485	−0.374743	−	0.927129i	$-0.622269\pi$
$653$	−19.1522	−0.749485	−0.374743	+	0.927129i	$0.622269\pi$
$654$	−6.68401	−0.261365
$655$	1.08802	0.0425123
$656$	−4.13919	−0.161608
$657$	12.9712	0.506053
$658$	−31.1722	−1.21522
$659$	12.2404	0.476819	0.238410	−	0.971165i	$-0.423374\pi$
$659$	12.2404	0.476819	0.238410	+	0.971165i	$0.423374\pi$
$660$	1.39250	0.0542031
$661$	26.4168	1.02749	0.513746	−	0.857942i	$-0.328257\pi$
$661$	26.4168	1.02749	0.513746	+	0.857942i	$0.328257\pi$
$662$	16.3254	0.634506
$663$	108.912	4.22979
$664$	−0.247349	−0.00959900
$665$	−8.84745	−0.343089
$666$	−16.3997	−0.635476
$667$	−15.5149	−0.600740
$668$	−11.9633	−0.462876
$669$	76.8433	2.97093
$670$	5.26369	0.203354
$671$	11.2032	0.432496
$672$	−15.3484	−0.592078
$673$	−42.1011	−1.62288	−0.811440	−	0.584436i	$-0.801316\pi$
$673$	−42.1011	−1.62288	−0.811440	+	0.584436i	$0.801316\pi$
$674$	−9.42295	−0.362959
$675$	75.3667	2.90087
$676$	30.1257	1.15868
$677$	−25.0456	−0.962581	−0.481290	−	0.876561i	$-0.659832\pi$
$677$	−25.0456	−0.962581	−0.481290	+	0.876561i	$0.659832\pi$
$678$	−34.4435	−1.32280
$679$	4.68111	0.179644
$680$	−2.03174	−0.0779135
$681$	4.72289	0.180981
$682$	1.05732	0.0404869
$683$	−2.75282	−0.105334	−0.0526668	−	0.998612i	$-0.516772\pi$
$683$	−2.75282	−0.105334	−0.0526668	+	0.998612i	$0.516772\pi$
$684$	36.4691	1.39443
$685$	3.04044	0.116169
$686$	37.0406	1.41422
$687$	9.75206	0.372064
$688$	−11.0527	−0.421380
$689$	−88.8579	−3.38522
$690$	7.71771	0.293808
$691$	37.0841	1.41075	0.705373	−	0.708837i	$-0.250780\pi$
$691$	37.0841	1.41075	0.705373	+	0.708837i	$0.250780\pi$
$692$	9.13150	0.347127
$693$	38.3607	1.45720
$694$	−19.2622	−0.731184
$695$	−6.00466	−0.227770
$696$	−8.68090	−0.329048
$697$	−20.9367	−0.793034
$698$	−23.1715	−0.877054
$699$	−32.6830	−1.23618
$700$	22.6503	0.856100
$701$	−21.4717	−0.810975	−0.405487	−	0.914101i	$-0.632898\pi$
$701$	−21.4717	−0.810975	−0.405487	+	0.914101i	$0.632898\pi$
$702$	−102.288	−3.86059
$703$	9.95637	0.375512
$704$	−1.05732	−0.0398493
$705$	8.77018	0.330304
$706$	−16.8980	−0.635963
$707$	−19.4005	−0.729630
$708$	−18.5870	−0.698544
$709$	4.56452	0.171424	0.0857121	−	0.996320i	$-0.472683\pi$
$709$	4.56452	0.171424	0.0857121	+	0.996320i	$0.472683\pi$
$710$	4.92603	0.184871
$711$	−94.4157	−3.54086
$712$	−17.0421	−0.638678
$713$	5.86002	0.219460
$714$	−77.6347	−2.90541
$715$	2.78901	0.104303
$716$	−8.70893	−0.325468
$717$	−21.3344	−0.796749
$718$	−8.77235	−0.327381
$719$	−34.5782	−1.28955	−0.644775	−	0.764372i	$-0.723049\pi$
$719$	−34.5782	−1.28955	−0.644775	+	0.764372i	$0.723049\pi$
$720$	3.11319	0.116022
$721$	62.0371	2.31038
$722$	−3.14061	−0.116881
$723$	17.6799	0.657523
$724$	−18.4507	−0.685716
$725$	12.8108	0.475780
$726$	−32.4013	−1.20253
$727$	17.1747	0.636974	0.318487	−	0.947927i	$-0.396825\pi$
$727$	17.1747	0.636974	0.318487	+	0.947927i	$0.396825\pi$
$728$	−30.7409	−1.13933
$729$	62.3992	2.31108
$730$	−0.672239	−0.0248807
$731$	−55.9063	−2.06777
$732$	34.7417	1.28409
$733$	−47.2086	−1.74369	−0.871845	−	0.489782i	$-0.837076\pi$
$733$	−47.2086	−1.74369	−0.871845	+	0.489782i	$0.837076\pi$
$734$	6.53698	0.241284
$735$	−19.6403	−0.724443
$736$	−5.86002	−0.216003
$737$	13.8555	0.510375
$738$	32.0808	1.18091
$739$	−41.7229	−1.53480	−0.767402	−	0.641167i	$-0.778451\pi$
$739$	−41.7229	−1.53480	−0.767402	+	0.641167i	$0.778451\pi$
$740$	0.849926	0.0312439
$741$	101.316	3.72193
$742$	63.3398	2.32528
$743$	23.1958	0.850973	0.425486	−	0.904965i	$-0.360103\pi$
$743$	23.1958	0.850973	0.425486	+	0.904965i	$0.360103\pi$
$744$	3.27880	0.120207
$745$	−1.88337	−0.0690012
$746$	−13.6132	−0.498415
$747$	1.91708	0.0701423
$748$	−5.34810	−0.195546
$749$	−18.7115	−0.683705
$750$	−12.9576	−0.473145
$751$	48.6559	1.77548	0.887740	−	0.460346i	$-0.152275\pi$
$751$	48.6559	1.77548	0.887740	+	0.460346i	$0.152275\pi$
$752$	−6.65915	−0.242834
$753$	58.1000	2.11728
$754$	−17.3867	−0.633187
$755$	−1.85392	−0.0674711
$756$	72.9127	2.65181
$757$	−50.9001	−1.85000	−0.924998	−	0.379971i	$-0.875934\pi$
$757$	−50.9001	−1.85000	−0.924998	+	0.379971i	$0.875934\pi$
$758$	−20.7333	−0.753068
$759$	20.3152	0.737395
$760$	−1.89003	−0.0685587
$761$	−26.6115	−0.964665	−0.482332	−	0.875988i	$-0.660210\pi$
$761$	−26.6115	−0.964665	−0.482332	+	0.875988i	$0.660210\pi$
$762$	5.83916	0.211531
$763$	9.54270	0.345469
$764$	4.47412	0.161868
$765$	15.7470	0.569334
$766$	−32.9367	−1.19005
$767$	−37.2275	−1.34421
$768$	−3.27880	−0.118313
$769$	−6.60483	−0.238176	−0.119088	−	0.992884i	$-0.537997\pi$
$769$	−6.60483	−0.238176	−0.119088	+	0.992884i	$0.537997\pi$
$770$	−1.98806	−0.0716449
$771$	24.5775	0.885138
$772$	2.94492	0.105990
$773$	−25.8617	−0.930179	−0.465090	−	0.885264i	$-0.653978\pi$
$773$	−25.8617	−0.930179	−0.465090	+	0.885264i	$0.653978\pi$
$774$	85.6639	3.07913
$775$	−4.83866	−0.173810
$776$	1.00000	0.0358979
$777$	32.4765	1.16509
$778$	25.1038	0.900017
$779$	−19.4765	−0.697817
$780$	8.64883	0.309678
$781$	12.9667	0.463985
$782$	−29.6409	−1.05996
$783$	41.2387	1.47375
$784$	14.9128	0.532599
$785$	−1.08911	−0.0388722
$786$	8.88128	0.316785
$787$	−1.42305	−0.0507262	−0.0253631	−	0.999678i	$-0.508074\pi$
$787$	−1.42305	−0.0507262	−0.0253631	+	0.999678i	$0.508074\pi$
$788$	−26.3151	−0.937438
$789$	−35.6677	−1.26980
$790$	4.89315	0.174090
$791$	49.1747	1.74845
$792$	8.19478	0.291189
$793$	69.5831	2.47097
$794$	−30.2272	−1.07272
$795$	−17.8204	−0.632024
$796$	23.3659	0.828182
$797$	−11.3395	−0.401664	−0.200832	−	0.979626i	$-0.564365\pi$
$797$	−11.3395	−0.401664	−0.200832	+	0.979626i	$0.564365\pi$
$798$	−72.2201	−2.55656
$799$	−33.6831	−1.19162
$800$	4.83866	0.171072
$801$	132.085	4.66698
$802$	−8.93328	−0.315445
$803$	−1.76952	−0.0624451
$804$	42.9665	1.51531
$805$	−11.0185	−0.388351
$806$	6.56701	0.231313
$807$	57.9539	2.04007
$808$	−4.14442	−0.145800
$809$	−4.41840	−0.155343	−0.0776713	−	0.996979i	$-0.524748\pi$
$809$	−4.41840	−0.155343	−0.0776713	+	0.996979i	$0.524748\pi$
$810$	−11.1741	−0.392619
$811$	−14.0624	−0.493797	−0.246899	−	0.969041i	$-0.579411\pi$
$811$	−14.0624	−0.493797	−0.246899	+	0.969041i	$0.579411\pi$
$812$	12.3936	0.434931
$813$	−0.196243	−0.00688256
$814$	2.23724	0.0784154
$815$	−4.82436	−0.168990
$816$	−16.5847	−0.580580
$817$	−52.0071	−1.81950
$818$	−3.18372	−0.111316
$819$	238.258	8.32540
$820$	−1.66261	−0.0580608
$821$	−21.4296	−0.747897	−0.373948	−	0.927450i	$-0.621996\pi$
$821$	−21.4296	−0.747897	−0.373948	+	0.927450i	$0.621996\pi$
$822$	24.8185	0.865646
$823$	43.9375	1.53157	0.765783	−	0.643100i	$-0.222352\pi$
$823$	43.9375	1.53157	0.765783	+	0.643100i	$0.222352\pi$
$824$	13.2527	0.461678
$825$	−16.7744	−0.584009
$826$	26.5366	0.923325
$827$	5.93793	0.206482	0.103241	−	0.994656i	$-0.467079\pi$
$827$	5.93793	0.206482	0.103241	+	0.994656i	$0.467079\pi$
$828$	45.4182	1.57839
$829$	−1.86466	−0.0647625	−0.0323812	−	0.999476i	$-0.510309\pi$
$829$	−1.86466	−0.0647625	−0.0323812	+	0.999476i	$0.510309\pi$
$830$	−0.0993538	−0.00344862
$831$	84.2005	2.92088
$832$	−6.56701	−0.227670
$833$	75.4312	2.61354
$834$	−49.0149	−1.69725
$835$	−4.80538	−0.166297
$836$	−4.97510	−0.172067
$837$	−15.5760	−0.538384
$838$	−29.5038	−1.01919
$839$	4.49730	0.155264	0.0776320	−	0.996982i	$-0.475264\pi$
$839$	4.49730	0.155264	0.0776320	+	0.996982i	$0.475264\pi$
$840$	−6.16507	−0.212715
$841$	−21.9903	−0.758286
$842$	−20.6485	−0.711595
$843$	−77.4944	−2.66905
$844$	11.4085	0.392696
$845$	12.1007	0.416278
$846$	51.6118	1.77445
$847$	46.2590	1.58948
$848$	13.5309	0.464655
$849$	12.3512	0.423892
$850$	24.4747	0.839476
$851$	12.3995	0.425051
$852$	40.2102	1.37758
$853$	5.43018	0.185926	0.0929630	−	0.995670i	$-0.470366\pi$
$853$	5.43018	0.185926	0.0929630	+	0.995670i	$0.470366\pi$
$854$	−49.6004	−1.69729
$855$	14.6487	0.500976
$856$	−3.99724	−0.136623
$857$	−15.4327	−0.527170	−0.263585	−	0.964636i	$-0.584905\pi$
$857$	−15.4327	−0.527170	−0.263585	+	0.964636i	$0.584905\pi$
$858$	22.7661	0.777223
$859$	3.23673	0.110436	0.0552180	−	0.998474i	$-0.482415\pi$
$859$	3.23673	0.110436	0.0552180	+	0.998474i	$0.482415\pi$
$860$	−4.43959	−0.151389
$861$	−63.5300	−2.16510
$862$	15.4316	0.525603
$863$	−9.50794	−0.323654	−0.161827	−	0.986819i	$-0.551739\pi$
$863$	−9.50794	−0.323654	−0.161827	+	0.986819i	$0.551739\pi$
$864$	15.5760	0.529905
$865$	3.66789	0.124712
$866$	9.70789	0.329888
$867$	−28.1484	−0.955971
$868$	−4.68111	−0.158887
$869$	12.8801	0.436929
$870$	−3.48690	−0.118217
$871$	86.0565	2.91591
$872$	2.03855	0.0690342
$873$	−7.75051	−0.262315
$874$	−27.5736	−0.932692
$875$	18.4995	0.625396
$876$	−5.48736	−0.185401
$877$	54.6746	1.84623	0.923116	−	0.384522i	$-0.125634\pi$
$877$	54.6746	1.84623	0.923116	+	0.384522i	$0.125634\pi$
$878$	−25.7483	−0.868963
$879$	−96.4061	−3.25170
$880$	−0.424699	−0.0143166
$881$	10.5757	0.356304	0.178152	−	0.984003i	$-0.442988\pi$
$881$	10.5757	0.356304	0.178152	+	0.984003i	$0.442988\pi$
$882$	−115.582	−3.89184
$883$	26.1947	0.881522	0.440761	−	0.897624i	$-0.354709\pi$
$883$	26.1947	0.881522	0.440761	+	0.897624i	$0.354709\pi$
$884$	−33.2170	−1.11721
$885$	−7.46595	−0.250965
$886$	6.05812	0.203527
$887$	−48.2804	−1.62110	−0.810548	−	0.585672i	$-0.800831\pi$
$887$	−48.2804	−1.62110	−0.810548	+	0.585672i	$0.800831\pi$
$888$	6.93778	0.232817
$889$	−8.33652	−0.279598
$890$	−6.84537	−0.229457
$891$	−29.4135	−0.985389
$892$	−23.4364	−0.784710
$893$	−31.3339	−1.04855
$894$	−15.3736	−0.514169
$895$	−3.49816	−0.116931
$896$	4.68111	0.156385
$897$	126.177	4.21294
$898$	8.55022	0.285324
$899$	−2.64759	−0.0883019
$900$	−37.5021	−1.25007
$901$	68.4417	2.28012
$902$	−4.37646	−0.145720
$903$	−169.641	−5.64530
$904$	10.5049	0.349389
$905$	−7.41119	−0.246356
$906$	−15.1332	−0.502767
$907$	6.68535	0.221983	0.110992	−	0.993821i	$-0.464597\pi$
$907$	6.68535	0.221983	0.110992	+	0.993821i	$0.464597\pi$
$908$	−1.44043	−0.0478025
$909$	32.1213	1.06540
$910$	−12.3478	−0.409327
$911$	−44.1931	−1.46418	−0.732092	−	0.681206i	$-0.761456\pi$
$911$	−44.1931	−1.46418	−0.732092	+	0.681206i	$0.761456\pi$
$912$	−15.4280	−0.510872
$913$	−0.261527	−0.00865529
$914$	−32.4658	−1.07387
$915$	13.9549	0.461333
$916$	−2.97428	−0.0982729
$917$	−12.6797	−0.418721
$918$	78.7857	2.60032
$919$	−42.6650	−1.40739	−0.703694	−	0.710503i	$-0.748467\pi$
$919$	−42.6650	−1.40739	−0.703694	+	0.710503i	$0.748467\pi$
$920$	−2.35382	−0.0776033
$921$	89.6763	2.95494
$922$	−19.7026	−0.648869
$923$	80.5360	2.65088
$924$	−16.2282	−0.533869
$925$	−10.2384	−0.336636
$926$	13.8858	0.456316
$927$	−102.715	−3.37360
$928$	2.64759	0.0869112
$929$	30.3682	0.996348	0.498174	−	0.867077i	$-0.334004\pi$
$929$	30.3682	0.996348	0.498174	+	0.867077i	$0.334004\pi$
$930$	1.31701	0.0431865
$931$	70.1703	2.29974
$932$	9.96797	0.326512
$933$	−102.188	−3.34549
$934$	−24.8547	−0.813271
$935$	−2.14820	−0.0702536
$936$	50.8977	1.66364
$937$	54.5399	1.78174	0.890870	−	0.454258i	$-0.150096\pi$
$937$	54.5399	1.78174	0.890870	+	0.454258i	$0.150096\pi$
$938$	−61.3429	−2.00292
$939$	−16.3291	−0.532880
$940$	−2.67482	−0.0872429
$941$	51.2235	1.66984	0.834920	−	0.550371i	$-0.185514\pi$
$941$	51.2235	1.66984	0.834920	+	0.550371i	$0.185514\pi$
$942$	−8.89024	−0.289660
$943$	−24.2558	−0.789876
$944$	5.66886	0.184506
$945$	29.2872	0.952713
$946$	−11.6862	−0.379952
$947$	11.4305	0.371441	0.185720	−	0.982603i	$-0.440538\pi$
$947$	11.4305	0.371441	0.185720	+	0.982603i	$0.440538\pi$
$948$	39.9419	1.29725
$949$	−10.9905	−0.356766
$950$	22.7677	0.738683
$951$	93.8446	3.04312
$952$	23.6778	0.767402
$953$	26.7421	0.866261	0.433131	−	0.901331i	$-0.357409\pi$
$953$	26.7421	0.866261	0.433131	+	0.901331i	$0.357409\pi$
$954$	−104.872	−3.39535
$955$	1.79714	0.0581541
$956$	6.50679	0.210445
$957$	−9.17850	−0.296699
$958$	25.2636	0.816230
$959$	−35.4332	−1.14420
$960$	−1.31701	−0.0425063
$961$	1.00000	0.0322581
$962$	13.8955	0.448009
$963$	30.9807	0.998339
$964$	−5.39219	−0.173671
$965$	1.18290	0.0380789
$966$	−89.9420	−2.89384
$967$	2.12773	0.0684230	0.0342115	−	0.999415i	$-0.489108\pi$
$967$	2.12773	0.0684230	0.0342115	+	0.999415i	$0.489108\pi$
$968$	9.88207	0.317622
$969$	−78.0373	−2.50692
$970$	0.401675	0.0128970
$971$	6.26416	0.201026	0.100513	−	0.994936i	$-0.467952\pi$
$971$	6.26416	0.201026	0.100513	+	0.994936i	$0.467952\pi$
$972$	−44.4846	−1.42684
$973$	69.9781	2.24340
$974$	−11.7642	−0.376950
$975$	−104.186	−3.33661
$976$	−10.5959	−0.339165
$977$	−56.7648	−1.81607	−0.908033	−	0.418898i	$-0.862417\pi$
$977$	−56.7648	−1.81607	−0.908033	+	0.418898i	$0.862417\pi$
$978$	−39.3803	−1.25924
$979$	−18.0189	−0.575888
$980$	5.99009	0.191346
$981$	−15.7998	−0.504450
$982$	22.4750	0.717205
$983$	8.69294	0.277262	0.138631	−	0.990344i	$-0.455730\pi$
$983$	8.69294	0.277262	0.138631	+	0.990344i	$0.455730\pi$
$984$	−13.5716	−0.432646
$985$	−10.5701	−0.336792
$986$	13.3919	0.426485
$987$	−102.207	−3.25330
$988$	−30.9003	−0.983070
$989$	−64.7690	−2.05953
$990$	3.29164	0.104615
$991$	−31.5666	−1.00275	−0.501374	−	0.865231i	$-0.667172\pi$
$991$	−31.5666	−1.00275	−0.501374	+	0.865231i	$0.667172\pi$
$992$	−1.00000	−0.0317500
$993$	53.5278	1.69865
$994$	−57.4078	−1.82086
$995$	9.38549	0.297540
$996$	−0.811007	−0.0256977
$997$	48.2328	1.52755	0.763774	−	0.645484i	$-0.223344\pi$
$997$	48.2328	1.52755	0.763774	+	0.645484i	$0.223344\pi$
$998$	−13.1115	−0.415036
$999$	−32.9580	−1.04275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.2	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.2	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.27880 q^{3} +1.00000 q^{4} +0.401675 q^{5} +3.27880 q^{6} -4.68111 q^{7} -1.00000 q^{8} +7.75051 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.27880 q^{3} +1.00000 q^{4} +0.401675 q^{5} +3.27880 q^{6} -4.68111 q^{7} -1.00000 q^{8} +7.75051 q^{9} -0.401675 q^{10} -1.05732 q^{11} -3.27880 q^{12} -6.56701 q^{13} +4.68111 q^{14} -1.31701 q^{15} +1.00000 q^{16} +5.05816 q^{17} -7.75051 q^{18} +4.70538 q^{19} +0.401675 q^{20} +15.3484 q^{21} +1.05732 q^{22} +5.86002 q^{23} +3.27880 q^{24} -4.83866 q^{25} +6.56701 q^{26} -15.5760 q^{27} -4.68111 q^{28} -2.64759 q^{29} +1.31701 q^{30} +1.00000 q^{31} -1.00000 q^{32} +3.46674 q^{33} -5.05816 q^{34} -1.88028 q^{35} +7.75051 q^{36} +2.11595 q^{37} -4.70538 q^{38} +21.5319 q^{39} -0.401675 q^{40} -4.13919 q^{41} -15.3484 q^{42} -11.0527 q^{43} -1.05732 q^{44} +3.11319 q^{45} -5.86002 q^{46} -6.65915 q^{47} -3.27880 q^{48} +14.9128 q^{49} +4.83866 q^{50} -16.5847 q^{51} -6.56701 q^{52} +13.5309 q^{53} +15.5760 q^{54} -0.424699 q^{55} +4.68111 q^{56} -15.4280 q^{57} +2.64759 q^{58} +5.66886 q^{59} -1.31701 q^{60} -10.5959 q^{61} -1.00000 q^{62} -36.2810 q^{63} +1.00000 q^{64} -2.63780 q^{65} -3.46674 q^{66} -13.1044 q^{67} +5.05816 q^{68} -19.2138 q^{69} +1.88028 q^{70} -12.2637 q^{71} -7.75051 q^{72} +1.67359 q^{73} -2.11595 q^{74} +15.8650 q^{75} +4.70538 q^{76} +4.94944 q^{77} -21.5319 q^{78} -12.1819 q^{79} +0.401675 q^{80} +27.8189 q^{81} +4.13919 q^{82} +0.247349 q^{83} +15.3484 q^{84} +2.03174 q^{85} +11.0527 q^{86} +8.68090 q^{87} +1.05732 q^{88} +17.0421 q^{89} -3.11319 q^{90} +30.7409 q^{91} +5.86002 q^{92} -3.27880 q^{93} +6.65915 q^{94} +1.89003 q^{95} +3.27880 q^{96} -1.00000 q^{97} -14.9128 q^{98} -8.19478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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